A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If fi is the radius of the earth, the maximum height attained by the body is

Question

Infinity Learn · Accepted Answer

initial K.E. $$=12mv2=12mve22=18mve2=GmM4R$$ ∵$$ve=2MGRP$$.E.$$=$$−GmMRTotal Energy $$=GmM4R$$−$$GmMR=$$−$$3GmM4R$$……………….(1)Lot$$ the body come to rest at a height r from the centre of the earth. Now its energy is given by Final $$energy=$$−GmMr………..$$(2)Comparing$$ eqs. $$(1) and (2), we $$getr=(4R/3)$$∴Maximum height $$attained=r$$−$$R=(4R/3)$$−$$R=(R/3)$$

A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If fi is the radius of the earth, the maximum height attained by the body is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material